Stability analysis of a mathematical model in a microcosm with piecewise constant arguments.

In this paper, we have modeled a population density of a bacteria species in a microcosm by using a differential equation, [Formula in text] where t ≥ 0, the parameters r, α, ß(0) and ß(1) denote positive numbers ann [t] denotes the integer part of [Formula in text]. First, to obtain the local and global behaviors, the boundedness character and the periodic nature of the population density for bacteria, discrete solutions of differential Eq. (A) is investigated. Examinations of the stability characterization of (A) show that increasing of the population growth rate decreases the local stability of the positive equilibrium point. Due to this result we need to consider a second approximation to obtain stability of population density. This can be performed at low density by incorporating an Allee function to (A) at time t. For the theoretical results obtained here we give an example by taking some parameter values from experimental data of bacteria populations [8] and show that the experimental and theoretical results for both models with and without Allee effect are in good agreement.

Frequency of cavum veli interpositi in non-psychotic population: a magnetic resonance imaging study.

This prospective MRI investigation was performed to determine the incidences of the cavum veli interpositi (CVI) in 505 (242 Male, 263 Female) non-psychotic persons. The mean age of the population was 39,179 +/- 0,904 (40,461 +/- 1,395 Male, 38 +/- 1,166 Female). There was no significant difference between the means of age in male and female groups (t-test, DF=479, p>0,05). The incidences of the CVI were 5.77%, 1.89%, 5.66%, 8.24%, 5%, 4.55%, 7.94%, 3.03% for age group of 0-9, 10-19, 20-29, 30-39, 40-49, 50-59, 60-69, 70-79 respectively. There was no significant difference between the incidences of the CVI in age-groups (chi(2)=3.804, DF=7, p>0.05). The incidences of the CVI were 5.54%, 6.61%, 4.56% for whole, male, and female populations respectively. There was no significant difference between the incidences of the CVI in both sexes (chi(2)=1.01, DF=1, p>0.05).

Height of normal pituitary gland on MRI: differences between age groups and sexes.

In this study, the coronal and sagittal heights of the pituitary glands were measured by magnetic resonance imaging (MRI) technique in 201 individuals. There was no sellar or parasellar region pathology in the study group. The data were evaluated according to age and sex groups. In all cases the coronal and sagittal heights of the pituitary glands were equal. The mean values of the coronal and sagittal heights in females (6.1 +/- 0.1 mm, 6.1 +/- 0.1 mm respectively) were higher than in males (5.7 +/- 0.2 mm, 5.6 +/- 0.2 mm respectively). The highest values for the coronal and sagittal heights were in the 11-20 years age group in both sexes. A gradual increase in the coronal and sagittal heights of the pituitary glands in the 0-10, 11-20 age groups was present in both sexes. Decrease in the heights of the pituitary glands was noted after 20 years of age onwards. Nevertheless there was a conspicuous increase in the mean value of the pituitary glands' heights in the 51-60 years age group in males. In females, a minimal increase in the mean value of the pituitary glands' heights was observed in the 61 years and over age group.

Frequency of septum pellucidum anomalies in non-psychotic population: a magnetic resonance imaging study.

This prospective MRI investigation was performed to investigate septum pellucidum (SP) anomalies in 505 (242 male, 263 female) non-psychotic persons. The mean age of the population was 39.179 +/- 0.904 (40.461 +/- 1.395 male, 38 +/- 1.166 female). There was no significant difference between the means of age in the male and female groups (t-test, DF = 479, p > 0.05). The SP anomalies were classified as cavitation anomalies (Type I) and absence of the SP (Type II). Type I anomalies were subdivided into four groups as isolated cavum septi pellucidi (Ia), cavum septi pellucidi et cavum vergae (Ib), anterior small triangular cavities (Ic), and cysts of the SP (Id). The incidences of the anomalies (Type I + Type II) were 17.31%, 1.89%, 7.55%, 3.53%, 7%, 4.55%, 4.76% and 6.06% for the age groups of 0-9, 10-19, 20-29, 30-39, 40-49, 50-59, 60-69 and 70-79 years respectively. The anomalies were very significantly more frequent in the 0-9 years age group than in the other age groups (chi 2 = 9.7858, DF = 1, p < 0.05). The incidences of the anomalies (Type I + Type II) were 6.34%, 5.37%, 7.22% for the whole, male, and female populations, respectively. These values were 1.39%, 1.65% and 1.14% for Type Ia, 2.77%, 2.89% and 2.66% for Type Ib, and 1.78%, 0.83% and 2.66% for Type Ic. Both Type Id and II anomalies were determined in only one case for each group in females (0.2%). There was no significant difference between the incidences of the anomalies in both sexes (chi 2 = 0.45, DF = 1, p > 0.05).

Arteriovenous malformation of the choroid plexus.

A case of a 55-year-old female with arteriovenous malformation (AVM) of the choroid plexus within the right ventricle is reported. Arteriovenous malformation of the choroid plexus is a rare occurrence. The MR findings of this malformation are discussed.

Magnetic resonance imaging in evaluation of congenital and acquired superior oblique palsy.

BACKGROUND: According to the recently popularized classification of superior oblique (SO) palsy based on congenital variations of the tendon, the primary pathology is the abnormality of the SO tendon rather than an innervational problem in congenital cases. If this hypothesis is true, denervation atrophy of SO muscle should not occur in patients with congenital SO palsy. METHODS: Eight patients with traumatic and nine patients with definite congenital SO palsy underwent magnetic resonance imaging (MRI) of the orbit. SO muscle width and cross-sectional area measurements were taken from coronal images and compared with the clinically uninvolved superior oblique muscles. RESULTS: Atrophy of varying degrees was observed in the SO muscle both in congenital and acquired cases. No significant difference was found in the appearance of the SO muscle between acquired and congenital SO palsy groups. CONCLUSION: We have been unable to demonstrate abnormalities of the SO tendon in both groups. The MRI appearance of the SO muscle suggested that in congenital SO palsy, the pathology is not limited to the tendon; there also is an abnormality of the muscle itself.